30 c 19 g 4, 4 30 12 30 19, 2 30 f 16 0 8 a 0 2 12 20 30 90 30 80 0
a 0 u 4 19 88 30 0 20 4 a 16 0 30

France · mixed homophonic alphabet · 1644 · read by others, verified here

Sir Richard Forster, 13 May 1644

Archives départementales du Val-d’Oise, 68.H.8, troisième liasse · published by Karen Britland (2013) · transcribed by S. Tomokiyo (2021)

Read by George Lasry, Norbert Biermann and Robert Pitt before this session. Here: a permutation control, a blind recovery of 31 of 34 symbols, and the reason the obvious attack fails

Daniel Bourdeau · resolved · updated

Summary. Tomokiyo’s page of unsolved ciphers still carries this passage, but it had been read: by Lasry after Britland’s article, independently by Biermann, and again in September 2026 by Pitt, whose key is public. Nothing about the text is new here, and no decipherment is claimed. What this page records is a verification and a lesson. The tracker had predicted a regular Stuart key of the Ormonde or Boswell type; the passage is instead a mixed homophonic alphabet of 34 symbols, 18 numbers and 16 letters, over 207 tokens in 37 comma-separated words. Pitt’s key stands 8.8 standard deviations above 20,000 permutations of the letter identities. A homophonic annealer with a French 5-gram model then recovers the key blind — 202 of 207 tokens, 31 of 34 symbols — but only once the training text writes u for v and i for j as a 1644 hand does. Before that change the same solver reads five of six matched controls and still fails the target, with a wrong key outscoring the truth: the plaintext, not the cipher, was outside the model. Status: verified. Four single slips and two one-occurrence words need the manuscript; priority is Lasry’s, Biermann’s and Pitt’s.

01 The passage

Britland’s 2013 article printed the ciphered passage from Forster’s papers, with two clear French passages and the date; Tomokiyo transcribed it on his blog on 21 September 2021 and Pitt’s input is token for token the same. The tracker row here had said “134 groups, 24 symbols”; the real counts:

tokenswordsdistinct symbolsnumberslettersseen onceIC
20737340 2 4 5 7 8 12 14 16 19 20 30 40 50 70 80 88 90a b c d e f g l n p q s t u x y80.047

Commonest: 30 (×24), 2 and 0 (×18 each), 20 (×13), x (×10), c and s (×9). The commas are word or word-pair boundaries, which is what makes 207 tokens tractable at all.

02 The key (Pitt; Lasry and Biermann earlier)

lettersa d · b t · c l · d i · e g · f b · g y · l r · n f · p a · q c · s o · t n · u m · x s · y p
numbers0 e · 2 e · 4 a · 5 g · 7 d · 8 t · 12 c · 14 z · 16 i · 19 n · 20 r · 30 u · 40 s · 50 t · 70 f · 80 l · 88 q · 90 p

No shift, no block, no odd/even row: a mixed alphabet with a second symbol (for t a third) for the frequent letters e a c d f g i l n p r s t, and u single although it is the commonest letter. The family is the Richelieu type of homophonic alphabet, not the regular Stuart type; the unused values presumably cover h k m o x and more homophones in the full key.

il ny a aucun subiet descrupule de manquer a dieu | ie vous en responds et mesmes dans | les reigles de perfection prenez sdulement les uoyes de prudence piur conceruer uotre uie pour en faire a dieu un plus grand sacrifiye par la multiplication des uos seruices pour le salut de uos freres | et mesurer a cela sil est meilleur d’agir, ou de soupir · 13. de may. 1644

There is no ground for scruple about failing God; I answer for it, even within the rules of perfection. Take only the ways of prudence to preserve your life, so as to make God a greater sacrifice of it by multiplying your services for the salvation of your brethren, and measure by that whether it is better to act or to suffer. Four tokens (bold) conflict with the reading — a→d, 16→i, q→c, g→y, each against several agreeing occurrences — and are single slips of the encipherer or of the typeset transcription; four in 207 is Boswell’s rate. Britland’s correspondents read aucune voie de scrupule and preveu seulement where Pitt reads aucun subiet and prenez; the tokens at issue (f, 14) occur once each and cannot be settled from the text.

03 Permutation control

The twenty plaintext-letter identities were permuted over Pitt’s homophone partition 20,000 times and the 207-letter decode scored with a French 5-gram model.

modelPitt’s keynull mean / sd / bestznull at least as good
letters only (6.5 M letters)−450.3−1327 / 117 / −9607.50 / 20,000
letters + word edges, u for v, i for j−524.9−1768 / 142 / −12308.80 / 20,000

04 Blind recovery, and what the controls say

A homophonic annealer (34 symbols to 26 letters, 150,000 steps, 8–12 restarts), first without and then with the word boundaries, on the target and on six matched controls: held-out French of 207 letters enciphered with a random key of exactly Pitt’s homophone multiplicities, adjacent words merged with probability 0.2 as in the target.

runmodelcontrols read (of 6)target
15-gram, letters only, no word edges0 (16–49 % right; the solver’s optimum beats the truth on 5 of 6)gibberish, 31 % of Pitt’s key
25-gram with spaces, raw corpus3 at 99.5–100 %; 3 fall into an all-i attractor from OCR Roman numeralsattractor
3same, Roman numerals removed5 at 99–100 %, one at 44 %−591.6 found against −602.4 for Pitt: a wrong key outscores the truth, 14.5 % agreement
4same, training text with vu, ji6 of 6 (98–100 %)97.6 % of Pitt’s key blind: 202 of 207 tokens

Run 1 is the lesson of the Moray letter at this length: 207 letters over 34 symbols with a plain letter-stream model is below the solver’s threshold even on controls, so nothing could have been read into a target failure. Run 3 is the more useful one: the controls pass and the target fails, so the plaintext was out of the model’s distribution. The letter writes uotre, uie, uos, seruices, uoyes, subiet, ie, as every 1644 hand does; a model trained on a nineteenth-century edition with v and j scores that spelling some 200 nats worse than modern French of the same length, and gibberish wins. Normalising the training text fixes it. The blind key differs from Pitt’s at three rare symbols only (g, 14, e), whose values n-grams cannot fix and the words do. The two 134-letter controls that were run under the same model (the tracker’s wrong length) both read at 97–99 %, so the length was never the obstacle.

05 What stays open

06 Method and files

  1. Tokeniser, groups, Pitt’s key and literal decode (forster/key.py).
  2. Letters-only French 5-gram, permutation test, blind annealer, six matched controls (ng5fr.py, solve.py, run1.txt).
  3. Word-edge model with u/v, i/j normalisation, same tests (solve2.py, run2–4.txt); the 134-letter repeat (control134.py, run5_134.txt).

Checked: Pitt’s input against the blog text; the key against 20,000 permutations; blind recovery and six matched controls under four models. Not checked: the manuscript; Britland’s article itself beyond its abstract and the readings quoted by Pitt.

07 Sources

Analysis scripts and the ciphertext are in the repository (forster/).